Buxton's bundled effort came just seconds after the Rams were denied a penalty when Michael Jacobs was brought down in the box.
Prior to that Paul Coutts had netted the rebound from a missed Conor Sammon spot kick, which came just six minutes after substitute Ross McCormack's 67th-minute opener for United.
As a result of the win Derby remain comfortable in mid-table and, although Leeds are one of the other sides in and around them, they are starting to slide.
This was their fifth game without a win and their unpopular manager Neil Warnock was serenaded with a number of expletive-laden chants throughout.
The lively finish to the game belied a dismal opening hour which offered little and showed just why neither of these sides have challenged the pacesetters this season.
Sammon received no backing as he appealed for an early penalty - he looked to have slipped as Jason Pearce approached - and that was the only noteworthy incident until the first shot came in the 33rd minute.
Leeds' Luke Varney had it, dragging well wide of Frank Fielding's goal after he got into some space on the left of the box, and although poor, the effort at least sparked the game up a little.
Minutes later Leeds' teenage debutant Chris Dawson helped tee up former Derby man Paul Green who cracked the bar from the edge of the box, while at the other end Paddy Kenny was quick off his line to close down Sammon after he beat Pearce to a neat through-ball from Chris Martin.
The momentum did not quite carry over into the second half, though, and it took until the 55th minute for another shot, with Kenny at his best to keep out Ben Davies from the edge of the box and Lee Peltier mopping up the rebound as Martin closed in.
Derby, improving more than their hosts, thought they had taken the lead with 63 minutes gone, as Peltier put a Martin cross through his own goal, but Sammon, no more than an inch ahead of him, was called offside.
Leeds brought McCormack off the bench as a bid to liven things up and the move reaped immediate dividends as the Scot opened the scoring with his first touch.
Stephen Warnock's corner from the right was not cleared and fell to McCormack, who, from his position just outside the area, cracked a first-time curler beyond Fielding and into the top corner.
Leeds' advantage would last just six minutes, though, as Derby got themselves deservedly back on level terms. Not for the first time Pearce was found short of pace and he bundled Martin to the floor, leaving Roger East with a simple decision to make.
Sammon took the responsibility of taking the penalty but proceeded to roll it onto the post, although fortunately for him Coutts was on hand to quickly adjust his body and whip in the second ball.
A second penalty should have followed as White brought down Jacobs six yards inside the area - East awarding a free-kick - but, after Davies' effort was saved by Kenny, the winger's subsequent corner was nodded in by Buxton.
- Sports & Recreation
- Conor Sammon
- Paul Coutts